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- Title
On constructions of Lie (super) algebras and (𝜀,δ)-Freudenthal–Kantor triple systems defined by bilinear forms.
- Authors
Kamiya, Noriaki; Mondoc, Daniel
- Abstract
In this work, we discuss a classification of (𝜖 , δ) -Freudenthal–Kantor triple systems defined by bilinear forms and give all examples of such triple systems. From these results, we may see a construction of some simple Lie algebras or superalgebras associated with their Freudenthal–Kantor triple systems. We also show that we can associate a complex structure into these (𝜀 , δ) -Freudenthal–Kantor triple systems. Further, we introduce the concept of Dynkin diagrams associated to such (𝜀 , δ) -Freudenthal–Kantor triple systems and the corresponding Lie (super) algebra construction.
- Subjects
DYNKIN diagrams; ALGEBRA; LIE algebras; LIE superalgebras; BILINEAR forms; CONSTRUCTION
- Publication
Journal of Algebra & Its Applications, 2020, Vol 19, Issue 11, pN.PAG
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498820502230